My research develops rigorous probabilistic and analytical frameworks for stochastic lattice and graph-based models arising in statistical mechanics and mathematical physics, with a focus on nonlocal and long-range interactions. I study scaling limits and fluctuation theory via (generalized) central and local limit theorems, establishing convergence of discrete random fields and interface models to continuum limits such as Gaussian and fractional Gaussian fields. Applications include long-range Ising models, interacting particle systems, reinforced stochastic processes, and Abelian sandpile models. A further direction concerns nonlocal geometry, including isoperimetric inequalities, minimal and equilibrium shapes. More recently, I have developed discrete realizations of conformal and logarithmic conformal field theories, providing new tools for the analysis of universality and criticality in discrete stochastic systems.

In particular, I am fascinated by the following research themes:

• Limit theorems for generalized Gaussian fields

• Discrete-to-continuum scaling limits of random fields

• (Non)-local isoperimetric inequalities and equilibrium shapes

• Phase transitions in long-range spin systems

• Sandpile models and (logarithmic) conformal field theory

• Synchronization and self-organisation

• Criticality on random graphs

• Reinforced random processes

PhD Students

• Kai-Chun Huang (2024-), together with Noela Mueller and Remco van der Hofstad

• Tess van Leeuwen (2024-)

• Alan Rapoport (2020-2024)

• Leandro Chiarini (2017-2021)

• Bruno Kimura (2015-2019)

Postdocs

• Fabio Coppini (2023-) 

• Vanasse Jacquier (2023-2025)

• Delara Behzad (Jan-May 2024)

• Leandro Chiarini (2021-2023)